The nilpotent variety of W(1;n)p is irreducible

In the late 1980s, Premet conjectured that the nilpotent variety of any finite dimensional restricted Lie algebra over an algebraically closed field of characteristic (Formula presented.) is irreducible. This conjecture remains open, but it is known to hold for a large class of simple restricted Lie algebras, e.g. for Lie algebras of connected algebraic groups, and for Cartan series (Formula presented.) and (Formula presented.). In this paper, with the assumption that (Formula presented.), we confirm this conjecture for the minimal (Formula presented.)-envelope (Formula presented.) of the Zassenhaus algebra (Formula presented.) for all (Formula presented.).